Relationship of maxillary 3-dimensional posterior occlusal plane to mandibular spatial position and morphology

Introduction

The purpose of this study was to examine the relationship of the 3-dimensional (3D) posterior occlusal plane (POP) and the mandibular 3D spatial position. The relationship of the POP to mandibular morphology was also investigated.

Methods

Retrospective data from a convenience sample of pretreatment diagnostic cone-beam computed tomography scans were rendered using InVivo software (Anatomage, San Jose, Calif). The sample consisted of 111 subjects (51 male, 60 female) and included growing and nongrowing subjects of different races and ethnicities. The 3D maxillary POP was defined by selecting the cusp tips of the second premolars and the second molars on the rendered images of the subjects. The angles made by this plane, in reference to the Frankfort horizontal plane, were measured against variables that described the mandibular position in the coronal, sagittal, and axial views. The POP was also compared with bilateral variables that described mandibular morphology.

Results

There were significant differences of the POP among the different skeletal malocclusions ( P <0.0001). The POP showed significant correlations with mandibular position in the sagittal ( P <0.0001), coronal ( P <0.05), and axial ( P <0.05) planes. The POP also showed a significant correlation with mandibular morphology ( P <0.0001).

Conclusions

These findings suggest that there is a distinct and significant relationship between the 3D POP and the mandibular spatial position and its morphology.

Highlights

  • Posterior occlusal plane (POP) differed significantly among different skeletal malocclusions.

  • POP was correlated with mandibular position in sagittal, coronal, and axial planes.

  • POP showed significant correlation with mandibular morphology.

  • 3D POP and mandibular spatial position and morphology were significantly related.

Early in the history of our specialty, both clinicians and researchers were aware of the relevance of the occlusal plane in the diagnosis and treatment of malocclusions. References to the occlusal plane can be found throughout the orthodontic literature. In 1947, Björk mentioned in his textbook that the steepness of the occlusal plane diminishes with prognathism. Bushra stated that the flatter the occlusal plane, “the more forward the face.” Downs, in 1948, noted that Class II malocclusions tend to have steeper occlusal planes, and Class III malocclusions have flatter occlusal planes. Riedel observed an apparent perpendicular relationship between the occlusal plane and the A-B plane in normal occlusions. Schudy, in 1963, mentioned the relationship of the occlusal plane to function and its significance in treatment. Several authors stated that Tweed obtained more favorable profiles because of his control of the occlusal plane by minimizing the untoward effects of Class II mechanics with his anchorage preparation.

The relationship of the occlusal plane to mandibular position continued to be observed as numerous studies, starting in the 1970s, began to show that during normal dentofacial development, both the occlusal plane and the mandibular plane flattened as the mandible rotated forward with growth. Sato et al demonstrated that the occlusal plane flattened excessively in growing patients with skeletal Class III malocclusions.

Traditionally, the occlusal plane was defined as a line from the incisors to the first molars. In a 1996 study, the authors proposed an alternative way to describe the curvature of the occlusal plane. They divided it into anterior and posterior components, with the anterior occlusal plane defined as a line drawn from the incisal edge of the maxillary central incisor to the cusp tip of the mandibular second premolar, and the posterior occlusal plane (POP) as a line from the cusp tip of the mandibular second premolar to the midpoint of the mandibular second molar at the occlusal surface.

These investigations have shown that the 2-dimensional (2D) POP correlates with anteroposterior mandibular position and predicts both Class II and Class III malocclusions. More recently, Tanaka and Sato conducted a longitudinal study using data from the Burlington Growth Center on white subjects and concluded that during normal Class I growth, the 2D POP flattens with age along with a concomitant decrease in the mandibular plane angle, as well as an increase in forward mandibular position. These findings are similar to previous studies with Japanese and African American samples. The occlusal plane has also been implicated in the different mandibular morphologies of high-angle Class II malocclusions compared with normal Class I and low-angle Class II malocclusions. A recent study with 3-dimensional (3D) cone-beam computed tomography (CBCT) data also found significant differences in the POP between Class II and Class III subjects.

From the coronal perspective, the cant of the POP has shown a distinct and significant relationship with a deviation of the chin from the midline and the mandibular lateral deviation. Researchers have found that the most common trait in facial asymmetries is a mandibular midline deviation. Most studies on mandibular lateral deviation have been conducted using posteroanterior cephalograms, which are reliable in evaluating asymmetries but have inherent inaccuracies because of difficulties in identifying anatomic structures, projection errors, and lack of reproducibility. There are also limitations to conventional 2D lateral cephalograms such as superimposition of bilateral structures and the inherent distortion of the radiograph. To improve on these limitations, CBCT can be used to more accurately analyze and study the 3D relationships of the various craniofacial structures. CBCT scans are on a 1:1 scale; therefore, there are no distortions associated with the data, and anatomic landmarks can more accurately be identified 3 dimensionally; this then provides the ability to select and measure bilateral structures with greater precision.

The purpose of this study was to examine the relationship of the 3D POP to mandibular spatial positioning as well as its morphology using CBCT data.

Material and methods

Three-dimensional data were obtained from CBCT scans taken of patients at the principal investigator’s private orthodontic practice (J.C.C.) as part of their pretreatment diagnostic records. The retrospective convenience sample consisted of 111 subjects (51 male, 60 female) and included growing and nongrowing subjects of different ethnicities. The selection criteria for the sample were patients (1) who signed the consent to use records section in the Informed Consent Form provided by the American Association of Orthodontists, (2) with fully erupted permanent dentition including maxillary second molars, (3) without syndromes or craniofacial anomalies, and (4) with no previous orthodontic treatment.

The sample was divided into Class I, Class II, and Class III based on the anteroposterior dysplasia indicator developed by Kim. The anteroposterior dysplasia indicator was selected over the more commonly used ANB angle because it considers both dentoalveolar and skeletal relationships that cannot be described by 1 measurement. The anteroposterior dysplasia indicator has been shown to have more diagnostic significance when comparing anteroposterior discrepancies. To take the vertical dimension into consideration, the Class II and Class III samples were further divided into high-angle and low-angle classifications based on the Frankfort horizontal plane to mandibular plane angle ( Table I ). Age and sex characteristics of the 5 groups were as follows: Class I (13 female, 10 male; mean age, 16.6 years; range, 11-41 years), high-angle Class II (14 female, 0 male; mean age, 17.2 years; range, 11-45 years), low-angle Class II (12 female, 14 male; mean age, 14.8 years; range, 11-39 years), high-angle Class III (11 female, 13 male; mean age, 20.5 years; range, 9-39 years), and low-angle Class III (10 female, 14 male; mean age, 20.7 years; range, 11-53 years).

Table I
Criteria for each class type
Class type APDI FMA (°)
Class I 78-82
Class II, high angle <78 >25
Class II, low angle <78 <25
Class III, high angle >83 >25
Class III, low angle >83 <25

APDI , Anteroposterior dysplasia indicator; FMA , Frankfort-mandibular plane angle.

The DICOM data were obtained using a Kodak 9500 Cone Beam 3D System (90 kW, full field of view: 200 × 184 mm, 0.3-mm voxel resolution, and 2-15 mA; Kodak, Rochester, NY) and was imported into and rendered with InVivo software (version 5.3.1; Anatomage, San Jose, Calif) to create a 3D image of the patient. The CBCT scans were taken with the patients standing up, with their heads positioned in Frankfort horizontal plane. The use of a custom-made cephalostat ensured that the interporion line was oriented parallel to the floor. This provided a standardized method for stabilizing the patient and diminished the need to reorient the scans in the software later.

All subjects were anonymized, and all patient identifiers were deleted. New InVivo files were created for each subject and assigned an identification number. The corresponding chronologic age and sex were recorded. Therefore, the retrospective research data did not contain any identifiable protected health information. The institutional review board of the University of Florida Health Center approved the research protocol.

Using the InVivo software, a 3D denture frame cephalometric analysis was developed with 33 landmarks ( Table II ). These landmarks were selected on the reconstructed 3D volume and then refined in the axial, coronal, and sagittal slices using the slice locator feature in the software. Landmarks were selected using an optical mouse on a 27-in iMac computer (Apple, Cupertino, Calif). Since the InVivo program was not yet available for Macintosh software, Boot Camp, a multiboot utility included in the Apple Operating System, version OS X 10.9, assisted in installing a 64-bit version of the Windows 7 operating system (Microsoft, Redmond, Wash). An operator (J.C.C.), who was previously calibrated, selected the anatomic landmarks and performed the cephalometric analysis.

Table II
Landmarks
Landmark Abbreviation Definition
Nasion N Midpoint of the frontonasal suture
Right orbitale Or R Most inferior point on the right infraorbital rim of the maxilla
Left orbitale Or L Lowest point on the left infraorbital rim of the maxilla
Medial orbitale Med Or Computer-generated medial (mean) point between the right and left orbitales
Right porion Po R Highest point on the upper margin of the right external auditory meatus
Left porion Po L Highest point on the upper margin of the left external auditory meatus
Sella turcica S Midpoint of the pituitary fossa
Basion Ba Midpoint of the anterior-inferior border of foramen magnum
Anterior nasal spine ANS Most anterior midpoint of the anterior nasal spine
Posterior nasal spine PNS Most posterior midpoint of the posterior nasal spine
A-point A Midpoint of the anterior limits of the apical base of the maxilla
Right condylion Co R Uppermost midpoint of the right condyle
Left condylion Co L Uppermost midpoint of the left condyle
Right gonion Go R Most lateral point on the right mandibular angle close to the bony gonion
Left gonion Go L Most lateral point on the left mandibular angle close to the bony gonion
Medial gonion Med Go Computer-generated medial (mean) point between the right and left gonions
Menton Me Midpoint of the lowest point on the mandibular symphysis
B-point B Midpoint of the anterior limits of the apical base of the mandible
Suprapogonion PM Midpoint of protuberance menti
Pogonion Pog Midpoint of the most anterior point of the mandibular symphysis
Right Xi point Xi R Point located on the geometric center of the right mandibular ramus
Left Xi point Xi L Point located on the geometric center of the left mandibular ramus
Medial Xi point Med Xi Computer-generated medial (mean) point between the right and left Xi points
U1 root tip U1 root R Maxillary right central incisor root tip
U1 incisal edge U1 crown R Midpoint on the incisal edge of the maxillary right central incisor
L1 root tip L1 root R Mandibular right central incisor root tip
L1 incisal edge L1 crown R Midpoint on the incisal edge of the mandibular right central incisor
Upper incisor point U1 Most mesial and incisal point of the maxillary left central incisor
U5 cusp tip U5 R Buccal cusp tip of the maxillary right second premolar
U7 cusp tip U7 R Distobuccal cusp tip of the maxillary right second molar
U5 cusp tip U5 L Buccal cusp tip of the maxillary left second premolar
U7 cusp tip U7 L Distobuccal cusp tip of the maxillary left second molar
Medial U5 Med U5 Computer-generated medial (mean) point between the right and left maxillary second premolar buccal cusp tips

A coordinate system was defined using a plane parallel to the Frankfort horizontal but going through sella as the horizontal reference plane. Since 3 points define 3D planes, a computer-generated medial point (mean) between the right and left orbitales was created. The right and left porions completed the definition of the Frankfort horizontal plane. Authors of a recent study found that there tends to be less variation in natural head posture in the coronal axis, possibly because the temporal bones house the organs of equilibrium, which impart the sensory input for the spatial orientation of the head. This makes the Frankfort horizontal plane a logical starting reference plane on the coronal axis. The sagittal reference plane is defined as a plane perpendicular to the horizontal reference plane passing through sella and nasion. The vertical reference plane is perpendicular to both the horizontal reference plane and the sagittal reference plane passing through sella ( Fig 1 ). The analysis consisted of 20 angular and 6 linear measurements ( Tables III and IV , respectively).

Fig 1
Three points define the Frankfort horizontal ( FH ) plane, the right and left porions and a computer-generated medial (mean) point between the right and left orbitales. The horizontal reference plane ( HRP ) is parallel to the Frankfort horizontal plane but goes through sella. The sagittal reference plane ( SRP ) is perpendicular to the horizontal reference plane passing through sella and nasion. The vertical reference plane ( VRP ) is perpendicular to both the horizontal reference plane and the sagittal reference plane passing through sella.

Table III
Angular measurements
Angular measurement Abbreviation Definition
Facial plane FP Na-Pog line and Frankfort horizontal (FH) plane
Line from A-point to B-point to mandibular plane AB-MP A-B line and Me-Med Go line
Sella to nasion to A-point angle SNA S-N line and Na-A point line
Sella to nasion to B-point angle SNB S-N line and N-B point line
A-point to nasion to B-point angle ANB N-A line and Na-B-point line
Anteroposterior dysplasia indicator APDI FP angle ± AB plane angle ± FH-PP
Mandibular lateral deviation MLD ANS-Me line and Ba-N-ANS plane
Frankfort horizontal to the mandibular plane angle FMA Me-Med Go line and FH plane
Gonial angle right Go R 3D angle made by the right Co-right Go line and right Go-Me line
Gonial angle left Go L 3D angle made by the left Co-left Go line and left Go-Me line
Condylar axis right Co axis R 3D angle made by the right Co-Xi point line and right Xi point- Me line
Condylar axis left Co axis L 3D angle made by the left Co-Xi point line and left Xi point-Me line
Palatal plane to Frankfort horizontal PP-FH ANS-PNS line and FH plane
Lower facial height LFHt ANS-Med Xi point and Med Xi point-PM line
Palatal plane to mandibular plane PP-MP ANS-PNS line and FMA line
Right posterior occlusal plane to Frankfort horizontal POP_R 3D angle made by the line formed by the points Med U5 point-U7 cusp tip _R line and FH plane
Left posterior occlusal plane to Frankfort horizontal POP_L 3D angle made by the line formed by the points Med U5 point-U7 cusp tip_L line and FH plane
Posterior occlusal plane cant POP cant 3D angle made by the line formed by the points U7 cusp tip _R –U7 cusp tip _L line and FH plane
Condylar cant Co cant 3D angle made by the Co_R-Co_L line and FH plane
Gonial cant Go cant 3D angle made by the Go_R-Go_L line and FH plane

Projected onto the sagittal reference plane; projected onto the vertical reference plane.

Table IV
Linear measurements
Linear measurement Abbreviation Definition
Mandibular length right MdL_R Distance between Go_R and Me
Mandibular length left MdL_L Distance between Go_L and Me
Ramus height right RamHt_R Distance between Co_R and Go_R
Ramus height left RamHt_L Distance between Co_L and Go_L
Condylar deviation Co dev Distance between the anteroposterior position of the right (−) vs the left (+) condylions, measured perpendicular to the vertical reference plane
Gonial deviation Go dev Distance between the anteroposterior position of the right (−) vs the left (+) gonions, measured perpendicular to the vertical reference plane

Projected onto the sagittal reference plane; projected onto the horizontal reference plane.

To define the 3D curved surface orientation of the maxillary occlusal plane, it was divided into anterior and posterior occlusal planes as described by Okuhashi et al. Occlusal landmarks were selected on the maxillary arch of the rendered 3D image as shown in Figure 2 . The POP was defined by 3 points. The first point was a computer-generated medial (mean) point between the right and left second premolar buccal cusp tips. The other 2 points were the distobuccal cusp tips of the second molars. To measure its effect on the right and left sagittal views, 2 lines were created from the medial point between the right and left second premolar buccal cusp tips to the distobuccal cusp tips of the second molars. These were defined as POP right and POP left. To measure this plane’s effect in the coronal and axial views, a third line was constructed from the distobuccal cusp tips of the second molars and named the POP cant ( Figs 2 and 3 ). This 3D definition of the POP measured against the Frankfort horizontal plane was then used to analyze its relationship to mandibular position and morphology ( Figs 2 and 3 ).

Fig 2
The POP is defined by 3 lines. The right and left POPs were created from a computer-generated medial (mean) point between the right and left second premolar buccal cusp tip to the distobuccal cusp tips of the right and left maxillary second molars. The third line of this plane was made from distobuccal cusp tips of the right and left second molars and named the POP cant . AOP , Anterior occlusal plane.

Fig 3
Depiction of the right and left POPs. Note the steep POP of the Class II skeletal morphology. AOP_R , Right anterior occlusal plane; AOP_L , left anterior occlusal plane.

To determine the spatial position of the mandible in the coordinate system, several variables were selected or created. The variables describing the mandibular anteroposterior, vertical, and transverse dimensions are listed in Table V . The anteroposterior and vertical variables were borrowed from conventional 2D analyses and projected onto the sagittal and vertical reference planes accordingly.

Table V
Descriptive and inferential statistics (°)
Variable Class I
Mean ± SD
(n = 23)
HA Class II
Mean ± SD
(n = 14)
LA Class II
Mean ± SD
(n = 26)
HA Class III
Mean ± SD
(n = 24)
LA Class III
Mean ± SD
(n = 24)
Shapiro-Wilk
P value
ANOVA
P value
Age (y) 16.5 ± 6.9 17.2 ± 9.3 14.8 ± 5.1 20.5 ± 11.3 20.7 ± 7.0 0.7 0.053
Anteroposterior
Facial plane 89.9 ± 2.0 85.3 ± 2.3 87.1 ± 2.5 92.6 ± 3.2 96.5 ± 3.2 0.1 <0.0001
APDI 80.6 ± 1.6 74.3 ± 2.7 74.0 ± 2.4 93.9 ± 7.5 99.2 ± 5.9 0.1 <0.0001
SNA 82.9 ± 2.0 82.6 ± 2.9 81.9 ± 3.5 81.6 ± 3.9 82.9 ± 3.1 0.9 0.481
SNB 79.3 ± 1.9 76.2 ± 2.1 76.5 ± 2.8 82.7 ± 4.0 85.7 ± 3.8 0.9 <0.0001
ANB 3.6 ± 1.1 6.4 ± 1.1 5.4 ± 1.5 −1.2 ± 2.5 −2.7 ± 2.2 0.9 <0.0001
Vertical
FMA 22.4 ± 5.3 31.9 ± 4.9 20.1 ± 4.0 29.7 ± 5.0 19.8 ± 3.1 0.1 <0.0001
PP-MP 24.3 ± 5.3 32.0 ± 4.9 22.5 ± 3.6 29.3 ± 4.9 20.6 ± 4.1 1.0 <0.0001
AB-MP 74.5 ± 5.2 73.3 ± 4.5 82.5 ± 2.9 56.5 ± 6.9 59.9 ± 5.3 0.1 <0.0001
LFHt 42.9 ± 4.5 47.2 ± 4.3 40.8 ± 3.8 48.5 ± 4.6 40.8 ± 3.9 0.1 <0.0001
Transverse
MLD −0.1 ± 3.6 −0.5 ± 2.1 −0.8 ± 3.1 −0.1 ± 2.9 −0.4 ± 3.8 0.1 0.63
Co cant 1.6 ± 1.4 0.3 ± 1.5 0.3 ± 1.7 0.3 ± 1.6 0.6 ± 1.9 0.4 0.05
Go cant 1.6 ± 1.9 0.5 ± 2.0 0.2 ± 2.1 0.4 ± 2.1 0.2 ± 1.8 0.3 0.06
Co dev 0.3 ± 2.7 0.2 ± 2.2 0.6 ± 2.0 −0.4 ± 5.8 1.3 ± 2.4 0.1 0.56
POP_L 14.3 ± 5.3 19.9 ± 5.3 15.8 ± 5.6 13.2 ± 6.0 9.9 ± 4.2 0.8 <0.0001
POP_R 17.3 ± 5.1 20.6 ± 3.4 15.6 ± 4.7 14.6 ± 6.2 9.6 ± 5.6 0.2 <0.0001
POP cant 0.3 ± 1.8 0.3 ± 1.7 0.1 ± 1.5 0.0 ± 2.0 −0.3 ± 2.6 0.5 0.62
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Apr 4, 2017 | Posted by in Orthodontics | Comments Off on Relationship of maxillary 3-dimensional posterior occlusal plane to mandibular spatial position and morphology
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